Joanna,
I envy you having all that naturally composted leafy material readily available. I think the main problem with grass clippings in a worm bin is that the decomposition raises the temperature above what worms can tolerate. My understanding is that they require a high carbon, low nitrogen environment. From "Organic Agriculture Centre of Canada":
"High protein/nitrogen levels can result in rapid degradation and its associated heating, creating inhospitable, often fatal, conditions. Heating can occur safely in the food layers of the vermiculture or vermicomposting system, but not in the bedding."
That would seem to indicate that the food source needs to be kept separate from the bedding and not mixed, contrary to what some articles seem to advise.